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According to the Survey of London, Peter Street, which is a small passage west of Wardour Street in Soho, probably gets its name from a saltpetre house which was built in 1656. "In 1720 Peter Street was described as 'a Street not over well inhabited', and in the 1830's as 'a short dirty street, without any thoroughfare'. By the late nineteenth century the buildings had become 'wretched hovels, and a disgrace to humanity'."
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As befitting an area which is a disgrace to humanity I have been unable to locate further information about the Crown and Thistle, though Horwood's map shows that a large brewery belonging to Sturkey and Co occupied a large plot at the end of the Peter Street. Whether the Crown and Thistle had any connection with the brewery is unknown.